Question

phys 111 - clickers - 2d motion
from the same height and at the same time, one ball is dropped and another is fired horizontally.
which ball has the greater velocity at ground level?
a. the “dropped” ball
b. the “fired” ball
c. they both have the same velocity on impact
d. it depends on how hard the ball was fired
e. it depends on the initial height

Explanation:

Step1: Analyze vertical motion

Both balls have the same initial vertical velocity ($v_{0y}= 0$) and fall from the same height $h$. Using the kinematic - equation $v_{y}^{2}=v_{0y}^{2}+2gh$, since $v_{0y} = 0$, the vertical component of the velocity of both balls when they hit the ground is $v_{y}=\sqrt{2gh}$.

Step2: Analyze horizontal motion

The dropped ball has no horizontal velocity ($v_{x}=0$). The fired ball has a non - zero horizontal velocity $v_{x}$.

Step3: Calculate the resultant velocity

The resultant velocity of a ball is given by $v=\sqrt{v_{x}^{2}+v_{y}^{2}}$. For the dropped ball, $v_{x} = 0$, so $v = v_{y}=\sqrt{2gh}$. For the fired ball, $v=\sqrt{v_{x}^{2}+2gh}$. Since $v_{x}>0$ for the fired ball, the magnitude of the velocity of the fired ball is greater than that of the dropped ball.

Answer:

B. The "fired" ball